Episode 25: Paths through space

Melinda sat on a lab stool, swinging her legs aimlessly. Nobody in the class wanted to risk arriving late to the lab and having Mathematician Nieminen cancel their next robo-duelling match, but avoiding that created a lot of downtime. At the end of the bench, Ken was staring intently at his notebook.

“How do you always manage to have something to do when we’re waiting for class?”

Ken sighed and looked up. “I may have bitten off more than I can chew with this project. You’d think modelling one measly electron would be doable, but it’s Earth-blighted hard.”

“So what are you doing, modelling the path of an electron? In an atom or something?”

“In a benzene molecule, because apparently that’s easier.” Ken grimaced. “But it doesn’t really have a path, because it’s quantum, and that’s just a mess. Heisenberg and what have you.” He yawned.

That sounded vaguely familiar. “Heisenberg’s principle, right? Is that the one that says if you’re being precise enough you can’t know both where something is and how it’s moving at the same time?”

“Yeah, that one. Obviously, if you’re measuring an electron you have to be quantum-level precise. But-” He paused to yawn again. “But if you know where an electron is at every point in time, you’d be able to work out how it was moving, right? So the electron can’t really have a path.”

“That’s pretty trippy.”

“Yeah, it’s all weird probability distributions that collapse when you make measurements and then somehow grow back again or something, I assume, and I have no idea how to write this up in a way that makes any sense at all.”

“Well, you wouldn’t be the first person to have that problem.” Ricardo had arrived early too, and peered over Ken’s shoulder at his notebook. “Interpretations of quantum mechanics are notoriously fickle. If it seems intuitive in one context, it’ll probably look outright impossible in another.”

“So they’re all just wrong?” Ken looked unimpressed.

“You could call them imperfect, rather. They can be helpful, if you’re aware of their limitations.”

“Like classical mechanics is useful, but it’s not really as accurate as quantum mechanics?” Melinda said.

“Hmm.” Ricardo stared up at the ceiling for a few moments. “Sort of, but not really. You can make measurements that show where classical mechanics breaks down. But our interpretations of quantum mechanics aren’t making predictions you can measure. They’re just tools to help us think about our mathematical predictions. The interpretations that are still considered legitimate are ones that haven’t been disproved by measurements. Sometimes they sound terribly unintuitive in ways that we haven’t — maybe can’t — use measurements to test, though.”

“So you’re saying the actual theory is just the maths?” Ken started making notes.

“You need a little bit of interpretation to get from an equation to a measurement. Otherwise you’d be doing pure mathematics, not physics and certainly not a modelling project. But if you can successfully predict whatever you set out to predict, your model works, doesn’t it?”

“You wouldn’t be the first person to have that problem either,” Ricardo said. “It’s worth some thought, but don’t beat yourself up about it. Nobody’s expecting you to have an intuitive grasp of quantum mechanics, believe me.”

Melinda glanced at her watch. The afternoon lab session was scheduled to start in less than a minute, but neither Bryony nor Kelly Jean had arrived yet. She kicked at the air nervously. Nieminen didn’t need much excuse to pull them out of the next robo-duelling match. Bryony might not understand the significance of that, but Kelly Jean knew it was the last match of the term and if her team — or Melinda’s — had to pull out, they’d be excluded from the rankings. She glanced at her watch again. Thirty seconds. Where were those girls?

Bryony rushed into the room, braids flying, and swung her bag onto the nearest lab bench. That was one. And Kelly Jean arrived moments later, as Bryony was pulling out a stool. She swerved to avoid Bryony, slipped on the smooth, hard floor, and landed with a thud. Melinda drew breath sharply. That hadn’t sounded pleasant.

“Bryony Adams, how dare you?” Melinda was relieved to see Kelly Jean getting back on her feet.

“I did noth-”

The click of Nieminen opening the door at the front of the lab seemed to echo through the laboratory. Melinda felt the adrenaline surge through her body and jumped to her feet. “Uh, good afternoon, Mathematician Nieminen!” It sounded weird and artificial, but it cut off the argument. It couldn’t be worth a robo-duelling ban, could it?

“Ah, yes, Mathematician. Everything, is, um, fine. I was just, um, sitting down here.” She jumped onto her lab stool, pulling her bag onto the floor with a resounding crash. Melinda’s heart sank. It obviously hadn’t been intentional, but Nieminen might not see it that way.

“No need to worry, Mathematician, we’ve got it under control.” Kelly Jean was on her knees, handing Bryony the contents of her bag. Melinda gawped.

“Alright class, no need to stare. I think we can trust the ladies to have a satchel under control. Remember that all of you need to make sure you’ve discussed the outline for your project write-up with an instructor before the end of today’s session.”

It wasn’t until they were leaving the lab that Melinda got chance to talk to Bryony. “What happened?”

Bryony scowled. “Dustborn caught us after lunch. He wanted to sort out some paperwork and refused to let us go until he’d finished. He took absolutely forever, so we had to sprint and, well, you saw the rest.”

“The hawk was an Earth animal that flew about watching everything very closely and then swooped down to devour some unsuspecting, innocent little creature.

Melinda giggled. “I’m not sure that’s the most flattering description.”

“Well, it wasn’t my fault I was late, was it? And then I had to wait excessively long to talk to von Rejk, because I was afraid she’d ask awkward questions if I got her to okay my outline, just to be told that innovation is a bad idea and I need to conform to established conventions.”

Melinda snorted. “What, did he insist that you use punctuation or something?”

“Hey, I use punctuation! I just wanted to start by throwing the data out and seeing what interesting conclusions you could get from it, but he insisted that I make the first thing the hypothesis and then consider the data strictly in terms of that. It’s so formulaic.”

“Yeah, but that’s the point, isn’t it?” Verashni came alongside them in the corridor. “If you do something that isn’t formulaic, you’ll get all your hopes that it’s interesting tangled up with whether or not it actually is interesting. But anyway, just wanted to say, nice save with Nieminen earlier. I barely missed Dustborn on my way out of the dining hall, but I didn’t think he’d keep you guys that long.”

“Yeah, well, I couldn’t wreck my first chance to see a robo-duelling match I actually care about, now could I? You guys had better win, is all.”